A novel particle–particle and particle–wall collision model for superellipsoidal particles

Abstract

In the framework of computational studies of particulate multiphase flow systems, either dilute or dense, particle–particle as well as particle–wall collisions need to be considered, which in the case of nonspherical particle shapes still presents a computational challenge. In this study, we present an efficient numerical implementation of a novel superellipsoidal particle collision model that can be used in general fluid flows. The superellipsoid shape formulation can be viewed as an extension of spherical or ellipsoidal shapes and can be used to represent spherical, ellipsoidal, cylindrical, diamond-like and cubic particles by varying solely five shape parameters. In this context, we present a fast, stable Newton–Raphson-based method for modeling frictional collisions of nonspherical superellipsoidal particles, and demonstrate the performance of our algorithms.

Coefficient of tangential restitution for non-spherical particles

“…In the literature, there are a variety of approaches that target nonspherical particles in collision problems, such as the polygon formulation, [4,5], discrete function representation (DFR), [6,7], continuous function representation (CFR), [7][8][9], and composite particles. Hogue and Newland, [4] investigated falling dominoes using the polygon formulation.…”

“…In addition, Feng and Owen, [5], investigated 2D polygon collisions and proposed a contact model for corner contacts. Another method to account for non-sphericity is the CFR method, in which the particle surface is expressed in a continuous fashion by employing a surface equation such as the superellipsoidal surface equation, [9]. Mustoe and Miyata, [10] used the CFR method in combination with the superellipsoid surface equation to study cube-shaped particles in a horizontal, rotating 2D cylinder, focusing on the relationship between the particle squareness and the dynamic angle of response.…”

“…In our previous work, [9], we discussed various techniques to account for nonsphericity of particles, such as polygon-shaped particles, multisphere composites, discrete function representation (DFR), and continuous function representation (CFR), where the last one proved to be superior in the scope of our work. In this context our previous work, [9], presented a novel frictional particle-wall and particleparticle collision model, applicable to any superellipsoidal particle collisions occurring in flows. The method proved to be efficient and robust even in the case where non-binary particle contacts occur, for example in filling processes, where a particle can be in contact with various other particles as well as the container wall.…”

“…The method proved to be efficient and robust even in the case where non-binary particle contacts occur, for example in filling processes, where a particle can be in contact with various other particles as well as the container wall. The method is based on a Lagrangian multiplier optimization technique in combination with the Newton-Raphson method, [9]. As no discretization of the particle surface is required, the approach is able to consider multitude of particles ( > 10 5 ) during thousands of time steps, [9].…”

“…The method is based on a Lagrangian multiplier optimization technique in combination with the Newton-Raphson method, [9]. As no discretization of the particle surface is required, the approach is able to consider multitude of particles ( > 10 5 ) during thousands of time steps, [9].…”